The Toffees manager has so far brought in Mason Holgate, Tom Cleverley and Gerard Deulofeu this summer, but needs further additions in order to improve on last season's poor campaign.
Even after signing Deulofeu from Barcelona, it appears that manager Martinez is keen to sign another winger, with reports of interest in signing Yarmolenko.
The Liverpool Echo report that Everton boss Martinez is a keen admirer of the 25-year-old wide man, and could even lodge a bid to sign him, having been alerted to his potential availability.
It's stated that Yarmolenko wants a move to the Premier League, and given Martinez's admiration for the player, a huge bid could be made by the Toffees.
With 71 goals in 177 games for Dynamo Kiev and 19 goals in 49 games for Ukraine, Yarmolenko has proven himself as a prolific winger - something Everton may well be in the market for.
Possessing superb technical ability as well as enough pace to trouble defences, Yarmolenko could give Everton another dangerous attacking option alongside the likes of Romelu Lukaku and Kevin Mirallas - if Martinez can stump up the cash to sign him.